Detectability of Large-Scale Solar Subsurface Flows

The accuracy of helioseismic measurement is limited by the stochastic nature of solar oscillations. In this article I use a Gaussian statistical model of the global seismic wave field of the Sun to investigate the noise limitations of direct-modeling analysis of convection-zone-scale flows. The theoretical analysis of noise is based on hypothetical data that cover the entire photosphere, including the portions invisible from the Earth. Noise estimates are derived for measurements of the flow-dependent couplings of global-oscillation modes and for combinations of coupling measurements that isolate vector-spherical-harmonic components of the flow velocity. For current helioseismic observations, which sample only a fraction of the photosphere, the inferred detection limits are best regarded as optimistic limits. The flow-velocity fields considered in this work are assumed to be decomposable into vector-spherical-harmonic functions of degree less than five. The problem of measuring the general velocity field is shown to be similar enough to the well-studied problem of measuring differential rotation to permit rough estimates of flow-detection thresholds to be gleaned from past helioseismic analysis. I estimate that, with existing and anticipated helioseismic datasets, large-scale flow-velocity amplitudes of a few tens of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\rm m\,s^{-1}}$\end{document} should be detectable near the base of the convection zone.